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BOND MATH: The Theory Behind the Formulas by Donald J. Smith

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Chapter 9: Bond Portfolios

Chapter 9 uses the simplifying assumption that all the bonds in the portfolio are valued on a coupon date so that the number of periods to final maturity, N, is an integer. To generalize, assume here that the valuation is between coupon payment dates. Let f be the fraction of the period that has gone by and (1 – f) be the fraction remaining. Note that f is equivalent to t/T in previous chapters. Here the day-count convention (i.e., actual/actual or 30/360) does not matter so simpler notation is used.

The market value for the portfolio is MV and now can include accrued interest. The future cash flows, which include coupon interest and principal redemptions, are summarized by CFn for n = 1 to N. These n do not have to ...

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